The work-energy theorem asserts that the total amount of work done by forces on an item equals the change in its kinetic energy. It is also known as the work-energy theorem, which holds that the work done by a particle equals the change in its kinetic energy. This concept may be extended to rigid bodies by defining the work done by the torque and the rotational kinetic energy produced by the body. 

The energy transferred to or from an item by applying force along a displacement is referred to as work.. Work may affect the potential energy of a device.

Body

What is work?

Essentially, the work done on a system is the product of all the components of force pointing in the direction of motion times the distance over which the force works. It is possible to represent work done in one-dimensional motion in the form of an equation as 

W=fdcos

where W denotes the amount of work done, F denotes the magnitude of the system’s force, d denotes the magnitude of the system’s displacement and denotes the angle between the force vector F and the displacement vector d.

Work Done may have a positive or negative value, or it might even be zero. 

• Positive work: When a force pushes an item in the direction of the force’s motion, the amount of work done is deemed positive. An example of this sort of work is the motion of a ball descending towards the ground. In this example the motion of the ball would be forward and hence work done would be positive.
• Negative work: When the direction of force and displacement are in opposition to one another, it is assumed that the work has a negative value.
• Zero work:The zero work done can be observed when The force acting on an item is perpendicular to the displacement of the object. The total amount of work done by the force on the object is zero in this case.

What is Energy?

Energy is defined as the ability to do work. Potential energy, kinetic energy, thermal energy, electrical energy, chemical energy, and nuclear energy are some of the several sources of energy available. 

Kinetic Energy:

• The sort of energy that an item or particle possesses as a consequence of its movement is referred to as kinetic energy. 
• When work is done on an object by exerting a net force on it, the object accelerates and accumulates kinetic energy as a consequence of the work being done on it. 
• Objects that are in motion along a straight line have Translational Kinetic Energy, whereas objects that are rotating around an axis have Rotational Kinetic Energy. The object can have Translational or rotational Kinetic Energy or both.

What is the Work-Energy Theorem?

According to the work-energy theorem, the net work done on an object by external forces is equal to the change in kinetic energy of the object. It’s vital to remember that the work-energy theorem takes into account net work done by all forces, not just one. Furthermore, it is evident from the preceding sentence as work done and kinetic energy are linked.

Work Done by Constant Force: Derivation of the Work 

The equation F = ma (Newton’s second law) describes the connection between the net force and the acceleration, and the displacement of a particle. In this section, we’ll look at the scenario when the resulting force F is constant in both magnitude and direction and is parallel to the particle’s motion.

v2f=v2i+2ad

(from the equation v2=u2-2as  where v denotes final velocity, u denotes starting velocity, and s denotes displacement )

We get,

d=v2f–v2i2a

as we know, the work done is given in terms of force is

W=Fd

Hence, the work done is given as

W=Fv2f–v2i2a

W=(ma)(v2f–v2i2a)

W=m(v2f–v2i2)

W=mv2f2–mv2i2

W=KEf–KEi

∆KE As a result, the total work done equals the change in Kinetic Energy. 

The Work-Energy Theorem has a variety of applications

The Work-Energy theorem’s application is that it is highly useful in assessing situations where a stiff body must move under many forces. Due to its rigid structure, a rigid body cannot store potential energy in its lattice and can only possess kinetic energy. The work done by any force which acts on a rigid body eventually equals the change in its kinetic energy, which is the foundation of the rigid body work-energy equation.

Conclusion

The term “work” is often used in everyday discourse, and we understand that it refers to the act of completing a task or doing a task. The Work-energy Theorem explains why there is such a thing as the Physics of No Work! Essentially, the work done on a system is the product of a constant force’s component pointing in the direction of motion times the distance over which the force works. This theorem asserts that the total work done by all forces acting on a particle equals the change in kinetic energy of the particle (or) The total work done by all forces acting on a system equals the change in kinetic energy of the system